![Copy content]()
sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5610, base_ring=CyclotomicField(8))
M = H._module
chi = DirichletCharacter(H, M([4,2,0,3]))
![Copy content]()
pari:[g,chi] = znchar(Mod(287,5610))
\(\chi_{5610}(287,\cdot)\)
\(\chi_{5610}(1277,\cdot)\)
\(\chi_{5610}(3323,\cdot)\)
\(\chi_{5610}(4973,\cdot)\)
![Copy content]()
sage:chi.galois_orbit()
![Copy content]()
pari:order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
\((1871,3367,1531,3301)\) → \((-1,i,1,e\left(\frac{3}{8}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(7\) | \(13\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) | \(47\) |
| \( \chi_{ 5610 }(287, a) \) |
\(1\) | \(1\) | \(e\left(\frac{3}{8}\right)\) | \(i\) | \(-i\) | \(e\left(\frac{7}{8}\right)\) | \(e\left(\frac{7}{8}\right)\) | \(e\left(\frac{3}{8}\right)\) | \(e\left(\frac{5}{8}\right)\) | \(e\left(\frac{5}{8}\right)\) | \(-1\) | \(i\) |
![Copy content]()
sage:chi.jacobi_sum(n)
